On the Bayesian analysis of the earthquake hazard in the North-East Indian peninsula

The Bayesian extreme-value distribution of earthquake occurrences has been used to estimate the seismic hazard in 12 seismogenic zones of the North-East Indian peninsula. The Bayesian approach has been used very efficiently to combine the prior information on seismicity obtained from geological data with historical observations in many seismogenic zones of the world. The basic parameters to obtain the prior estimate of seismicity are the seismic moment, slip rate, earthquake recurrence rate and magnitude. These estimates are then updated in terms of Bayes’ theorem and historical evaluations of seismicity associated with each zone. From the Bayesian analysis of extreme earthquake occurrences for North-East Indian peninsula, it is found that for T = 5 years, the probability of occurrences of magnitude (M _w = 5.0–5.5) is greater than 0.9 for all zones. For M _w = 6.0, four zones namely Z1 (Central Himalayas), Z5 (Indo-Burma border), Z7 (Burmese arc) and Z8 (Burma region) exhibit high probabilities. Lower probability is shown by some zones namely␣Z4, Z12, and rest of the zones Z2, Z3, Z6, Z9, Z10 and Z11 show moderate probabilities.     

Source Parameters of the Deadly M<Subscript>w</Subscript> 7.6 Kashmir Earthquake of 8 October, 2005

During the last six years, National Geophysical Research Institute, Hyderabad has established a semi-permanent seismological network of 5–8 broadband seismographs and 10–20 accelerographs in the Kachchh seismic zone, Gujarat with a prime objective to monitor the continued aftershock activity of the 2001 M_w 7.7 Bhuj mainshock. The reliable and accurate broadband data for the 8 October M_w 7.6 2005 Kashmir earthquake and its aftershocks from this network as well as Hyderabad Geoscope station enabled us to estimate the group velocity dispersion characteristics and one-dimensional regional shear velocity structure of the Peninsular India. Firstly, we measure Rayleigh-and Love-wave group velocity dispersion curves in the period range of 8 to 35 sec and invert these curves to estimate the crustal and upper mantle structure below the western part of Peninsular India. Our best model suggests a two-layered crust: The upper crust is 13.8 km thick with a shear velocity (Vs) of 3.2 km/s; the corresponding values for the lower crust are 24.9 km and 3.7 km/sec. The shear velocity for the upper mantle is found to be 4.65 km/sec. Based on this structure, we perform a moment tensor (MT) inversion of the bandpass (0.05–0.02 Hz) filtered seismograms of the Kashmir earthquake. The best fit is obtained for a source located at a depth of 30 km, with a seismic moment, Mo, of 1.6 × 10²⁷ dyne-cm, and a focal mechanism with strike 19.5°, dip 42°, and rake 167°. The long-period magnitude (M_A ~ M_w) of this earthquake is estimated to be 7.31. An analysis of well-developed sPn and sSn regional crustal phases from the bandpassed (0.02–0.25 Hz) seismograms of this earthquake at four stations in Kachchh suggests a focal depth of 30.8 km.     

Archaeomagnetic secular variation in the UK during the past 4000 years and its application to archaeomagnetic dating

This paper examines the limitations and deficiencies of the current British archaeomagnetic calibration curve and applies several mathematical approaches in an attempt to produce an improved secular variation curve for the UK for use in archaeomagnetic dating. The dataset compiled is the most complete available in the UK, incorporating published results, PhD theses and unpublished laboratory reports. It comprises 620 archaeomagnetic (directional) data and 238 direct observations of the geomagnetic field, and includes all relevant information available about the site, the archaeomagnetic direction and the archaeological age. A thorough examination of the data was performed to assess their quality and reliability. Various techniques were employed in order to use the data to construct a secular variation (SV) record: moving window with averaging and median, as well as Bayesian statistical modelling. The SV reference curve obtained for the past 4000 years is very similar to that from France, most differences occurring during the early medieval period (or Dark Ages). Two examples of dating of archaeological structures, medieval and pre-Roman, are presented based on the new SV curve for the UK and the implications for archaeomagnetic dating are discussed.     

A Least-squares Window Curves Method for Interpretation of Magnetic Anomalies Caused by Dipping Dikes

We have developed a least-squares method to determine simultaneously the depth and the width of a buried thick dipping dike from residualized magnetic data using filters of successive window lengths. The method involves using a relationship between the depth and the half-width of the source and a combination of windowed observations. The relationship represents a family of curves (window curves). For a fixed window length, the depth is determined for each half-width value by solving one nonlinear equation of the form f (z) = 0 using the least-squares method. The computed depths are plotted against the width values representing a continuous curve. The solution for the depth and the width of the buried dike is read at the common intersection of the window curves. The method involves using a dike model convolved with the same moving average filter as applied to the observed data. As a result, this method can be applied to residuals as well as to measured magnetic data. Procedures are also formulated to estimate the amplitude coefficient and the index parameter. The method is applied to theoretical data with and without random errors. The validity of the method is tested on airborne magnetic data from Canada and on a vertical component magnetic anomaly from Turkey. In all cases examined, the model parameters obtained are in good agreement with the actual ones and with those given in the published literature.     

Maximum-likelihood ambiguity resolution based on Bayesian principle

 Based on the Bayesian principle and the fact that GPS carrier-phase ambiguities are integers, the posterior distribution of the ambiguities and the position parameters is derived. This is then used to derive the maximum posterior likelihood solution of the ambiguities. The accuracy of the integer ambiguity solution and the position parameters is also studied according to the posterior distribution. It is found that the accuracy of the integer solution depends not only on the variance of the corresponding float ambiguity solution but also on its values. Received: 27 July 1999 / Accepted: 22 November 2000     

New analytical and numerical approaches for geopotential modeling

 The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential coefficients _n,m . In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal harmonic series is developed for the geopotential and then its coefficients _n,m ^e are transformed to the unknown _n,m . The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From two sets of _n,m (n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068) by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to apply the LS technique for evaluating geopotential coefficients. Received: 12 December 2000 / Accepted: 21 June 2001     

Risk assessment for the Yucca Mountain high-level nuclear waste repository site: Estimation of volcanic disruption

In this article, we model the volcanism near the proposed nuclear waste repository at Yucca Mountain, Nevada, U.S.A. by estimating the instantaneous recurrence rate using a nonhomogeneous Poisson process with Weibull intensity and by using a homogeneous Poisson process to predict future eruptions. We then quantify the probability that any single eruption is disruptive in terms of a (prior) probability distribution, since not every eruption would result in disruption of the repository. Bayesian analysis is performed to evaluate the volcanic risk. Based on the Quaternary data, a 90% confidence interval for the instantaneous recurrence rate near the Yucca Mountain site is (1.85×10^–6/yr, 1.26×10^–5/yr). Also, using-these confidence bounds, the corresponding 90% confidence interval for the risk (probability of at least one disruptive eruption) for an isolation time of 10⁴ years is (1.0×10^–3, 6.7×10^–3), if it is assumed that the intensity remains constant during the projected time frame.     

任意点震源τ-P域地震图的解及AVO分析

用严格的数学推导得出τ-P域地震图的解析解。分析表明,τ-P域中地震图的子波可表示为激发震源子波的积分形式,决定反射波振幅的因素是平面波反射系数、反射界面上覆介质的波速以及方向因子。这些结果说明:1.在τ-P域进行AVO分析是可行的,并具有更高的精度;2.从一种新的途径可以进行速度函数的反演计算。